| clear,clc
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| addpath('files');
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| load('model')
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| n_e=model.n_e;
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| [n_nodes,nodes,weights] = Monomials_2(n_e,eye(n_e));
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| nodes=nodes'; % transpose to n_e-by-n_nodes
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| %----------------------------------
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| % Make a vector of parameter values
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| %----------------------------------
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| BETA=.96; GAMMA=2; ALPHA=.3; RHO=.8; DELTA=.1; SIGMA=.02; PHI=0.1;
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| params=eval(symparams);
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| %------------------
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| % transition matrix
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| %------------------
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| transition=[.95,.05;
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| .5,.5];
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| %--------------------------------------------------------------------------
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| % Prepare an initial guess - perturbation solution of RBC without disasters
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| %--------------------------------------------------------------------------
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| fixed_markov_values=0; % start with a fixed value for the disaster shock (disaster shock is 0 in all states)
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| % Steady state values
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| kss=((1/BETA-1+DELTA)/ALPHA)^(1/(ALPHA-1));
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| zss=0;
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| css=kss^ALPHA-DELTA*kss;
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| nxss=[log(kss);zss];
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| nyss=log(css);
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| % Cross moments of the shocks
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| M=get_moments(nodes,weights,model.order(2));
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| % Compute the perturbation solution
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| [derivs,stoch_pert,nonstoch_pert,model]=get_pert(model,params,M,nxss,nyss,fixed_markov_values);
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| % the variables stoch_pert and nonstoch_pert have two columns, corresponding to the two Markov states.
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| %-------------------------------------
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| % Taylor projection with Markov shocks
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| %-------------------------------------
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| markov_values=[0,1]; % now the values of the Markov shock depend on the Markov state
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| x0=nxss; % the approximation point
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| c0=nxss; % the center of the initial guess
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| % tolerance parameters for the Newton solver
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| tolX=1e-6;
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| tolF=1e-6;
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| maxiter=10;
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| % model.jacobian='exact'; % this is the default
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| % model.jacobian='approximate'; % for large models try the approximate jacobian.
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| initial_guess=stoch_pert;
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| [coeffs,model]=tpsolve(initial_guess,x0,model,params,markov_values,transition,c0,nodes,weights,tolX,tolF,maxiter);
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| %-------------------------------------------------------------------------------------
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| % Compute the residual function and the model variables at point x0 for Markov state s
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| %-------------------------------------------------------------------------------------
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| s=1; % Markov state 1
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| [R_fun1,g_fun1,Phi_fun1,auxvars1]=residual(coeffs,x0,params,markov_values,transition,c0,nodes,weights,s);
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| c1=exp(g_fun1); % consumption in normal state
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| inv1=exp(Phi_fun1(1,1))-exp(x0(1))*(1-DELTA);
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| s=2; % Markov state 2
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| [R_fun2,g_fun2,Phi_fun2,auxvars2]=residual(coeffs,x0,params,markov_values,transition,c0,nodes,weights,s);
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| c2=exp(g_fun2); % consumption in normal state
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| inv2=exp(Phi_fun2(1,1))-exp(x0(1))*(1-DELTA);
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| c2/c1-1 % fall in consumption is smaller than fall in output
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| inv2/inv1-1 % fall in investment is larger than fall in output
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| %-------------------
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| % Simulate the model
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| %-------------------
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| T=1000;
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| shocks=randn(1,T+1); % draw shocks
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| % simulate a Markov chain from the transition matrix
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| ushock=rand(1,T+1); % draw shocks from a uniform distribution to determine the Markov state
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| Markov_state=zeros(1,T+1);
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| Markov_state(1)=1; % start at state 1
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| for t=2:T+1
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| Markov_state(t)=1+(ushock(t)>transition(Markov_state(t-1),1)); % state in period t, given the state in t-1
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| end
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| % preallocate
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| x_simul=zeros(model.n_x,T+1);
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| y_simul=zeros(model.n_y,T);
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| R_simul=zeros(model.n_y,T);
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| x_simul(:,1)=x0;
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| for t=1:T
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| xt=x_simul(:,t);
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| st=Markov_state(t);
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| [Rt,yt]=residual(coeffs,xt,params,markov_values,transition,c0,nodes,weights,st);
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| epsp=shocks(t+1); % future iid shock
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| stp=Markov_state(t+1); % future Markov shock
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| y_simul(:,t)=yt;
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| x_simul(:,t+1)=evalPhi(xt,yt,epsp,stp,st,params,markov_values);
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| R_simul(:,t)=Rt;
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| end
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| |
